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UBC Theses and Dissertations

Modeling of linear systems with parameter variations : applications in hard disk and ball screw drives Sepasi, Daniel


This thesis considers variations in the parameters of the dynamics of linear systems, and tackles modeling of Linear Time-Invariant (LTI) and Linear Parameter Varying (LPV) plants. The variations in the dynamics make the controller design challenging, and to successfully overcome this challenge, two methods are proposed in this thesis. One method generates a connected model set. The idea of the multidimensional principal curves methodology is employed to detect the nonlinear correlations between parameters of the given set of system dynamics. The connected model set is simple and tight, leading to both nonconservatism and reduced computational complexity in subsequent controller design, and hence, to improve the controller performance. The other method is developed to derive a family of discrete model sets for a given set of system response data. A relaxed version of the normalized cut methodology is developed and used in an algorithm to divide a given set of system responses into the smallest possible number of partitions in such a way that a desired performance objective is satisfied for all partitions by designing one controller for each partition. Using the proposed method, a tight uncertainty model is derived for Hard Disk Drive (HDD) systems, and an H∞ controller is synthesized. The dynamics of HDDs is studied from a controller design point of view. Especially, the variations in the dynamics due to the change in temperatures and limited precision in the production line are examined. Also, the variations in the dynamics of Ball Screw Drive (BSD) systems due to the structural flexibility, runout, and workpiece mass variation are studied. These three factors are explicitly incorporated in LPV models. To build the LPV models, it is determined how the system parameters are affected by two variables, namely, the measurable table position and the uncertain mass of the table. We design robust gain scheduling controllers which are scheduled by the table position and are robust over the table mass.

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